Daniel is 28 years older than Jessica. Ten years ago, Daniel was 5 times as old as Jessica. How old is Jessica now?
Answer: We can use the given information to write down two equations that describe the ages of Daniel and Jessica. Let Daniel's current age be $d$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $d = j + 28$ Ten years ago, Daniel was $d - 10$ years old, and Jessica was $j - 10$ years old. The information in the second sentence can be expressed in the following equation: $d - 10 = 5(j - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to use our first equation for $d$ and substitute it into our second equation. Our first equation is: $d = j + 28$ . Substituting this into our second equation, we get the equation: $(j + 28)$ $-$ $10 = 5(j - 10)$ which combines the information about $j$ from both of our original equations. Simplifying both sides of this equation, we get: $j + 18 = 5 j - 50$ Solving for $j$ , we get: $4 j = 68$ $j = 17$.